Adam Clarke on Matthew 21:16

Out of the mouth of babes - The eighth Psalm, out of which these words are quoted, is applied to Jesus Christ in three other places in the new covenant, 1Cor 15:27; Eph 1:22; Heb 2:6. Which proves it to be merely a prophetic psalm, relating to the Messiah.

It was a common thing among the Jews for the children to be employed in public acclamations; and thus they were accustomed to hail their celebrated rabbins. This shouting of the children was therefore no strange thing in the land: only they were exasperated, because a person was celebrated against whom they had a rooted hatred. As to the prophecy that foretold this, they regarded it not. Some imagine that babes and sucklings in the prophecy have a much more extensive meaning, and refer also to the first preachers of the Gospel of Christ.